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3 years ago

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Andrew is painting a wall on the side of his house. He has a 20 foot ladder wich makes a 79 degree angle with the ground. Standi

ng on the second to past rung of the ladder, Andrew can reach 5 feet above the point where the ladder rests against the wall. How high up the wall can Andrew paint

1 answer:

torisob [31]3 years ago

3 0

Andrew can reach a maximum of $24.6ft$ high up the wall.

The right-angled triangle formed can be solved using the $sine$ ratio. that is

$sin(72^\circ})=\dfrac{h}{20}$

where $h$ is the distance from the foot of the wall to the tip of the ladder where it rests on the wall. Substituting, and solving for $h$ , we get

$0.9816=\dfrac{h}{20}\\\\h=20\times0.9816\\\\h=19.632ft$

Since Andrew can reach an extra $5ft$ above the point where the ladder rests against the wall, the maximum height Andrew can paint is

$(19.632+5)ft=24.632ft\\\\\approx24.6ft$

Another solved word problem on trigonometry can be found here: brainly.com/question/12146092

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For each target, there are only two possible outcomes. Either he hits it, or he does not. The probability of hitting a target is independent of other targets. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

In which $C_{n,x}$ is the number of different combinations of x objects from a set of n elements, given by the following formula.

$C_{n,x} = \frac{n!}{x!(n-x)!}$

And p is the probability of X happening.

0.95 probaiblity of hitting a target

This means that $p = 0.95$

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This means that $n = 10$

What is the probability that he will miss at least one of them?

Either he hits all the targets, or he misses at least one of them. The sum of the probabilities of these events is decimal 1. So

$P(X = 10) + P(X < 10) = 1$

We want P(X < 10). So

$P(X < 10) = 1 - P(X = 10)$

In which

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

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✩ Answer:

✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*

$\bold{Hello!}\\\bold{Your~answer~is~below!}$

✩ Step-by-step explanation:

✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*✧･ﾟ: *✧･ﾟ:*

✺ Divide both sides by −3. Since −3 is negative, the inequality direction is changed:

-3 ÷ -3 = Cancels Out
Turns into: $\frac{-9}{-3} >5x-2$

✺ Divide −9 by −3 to get 3. Since they are both negatives it turns into a positive:

-9 ÷ -3 = 3
Turns into: $3 > 5x - 2$

✺ Swap sides so that all variable terms are on the left hand side. This changes the sign direction once more:

Turns into: $5x-2$

✺ Add 2 to both sides:

Turns into: $5x$

✺ Add 3 and 2 to get 5:

3 + 2 = 5
Turns into: $5x$

✺ Divide both sides by 5. Since 5 is positive, the inequality direction remains the same:

5 ÷ 5 = Cancels Out
Turns into: $x$

✺ Divide 5 by 5 to get 1:

5 ÷ 5 = 1

✺ So your answer is B, $\boxed{x$ .

(Number line is below.)

$Hope~this~helps~and,\\Best~of~luck!\\\\~~~~~-TotallyNotTrillex$

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